| Remus | Aer | Tyro |
| Hama | Cortis | Merces |
| Sector | Ala | Mars |
| Sypho | Tergum | Oliva |
| Plebs | Pallor | Mora |
| Frenum | Uncus | Spicula |
| Saltus | Scena | Vestis |
| Moles | Bidens | Tibicen |
| Urna | Ostrum | Comes |
The sides, which touch the vertical plane in the first position, are respectively, in a c d Moena, in c d a Syce, in d a c Alvus.
Take the shape Urna, Ostrum, Moles, Saltus, Scena, Sypho, Remus, Aer, Tyro. This gives in a c d the projection: Urna Moena, Ostrum Moena, Moles Moena, Saltus Moena, Scena Moena, Vestis Moena. (If the different positions of the cube are not well known, it is best to have a list of the names before one, but in every case the block should also be built, as well as the names used.) The same shape in the position c d a is, of course, expressed in the same words, but it has a different appearance. The front face consists of the Syces of
| Saltus | Sypho | Remus |
| Moles | Plebs | Hama |
| Urna | Frenum | Sector |
And taking the shape we find we have Urna, and we know that Ostrum lies behind Urna, and does not come in; next we have Moles, Saltus, and we know that Scena lies behind Saltus and does not come in; lastly, we have Sypho and Remus, and we know that Aer and Tyro are in the Y direction from Remus, and so do not come in. Hence, altogether the projection will consist only of the Syces of Urna, Moles, Saltus, Sypho, and Remus.
Next, taking the position d a c, the cubes in the front face have their Alvus sides against the plane, and are:
| Sector | Ala | Mars |
| Frenum | Uncus | Spicula |
| Urna | Ostrum | Comes |
And, taking the shape, we find Urna, Ostrum; Moles and Saltus are hidden by Urna, Scena is behind Ostrum, Sypho gives Frenum, Remus gives Sector, Aer gives Ala, and Tyro gives Mars. All these are Alvus sides.
Let us now take the reverse problem, and, given the three cyclical projections, determine the shape. Let the a c d projection be the Moenas of Urna, Ostrum, Bidens, Scena, Vestis. Let the c d a be the Syces of Urna, Frenum, Plebs, Sypho, and the d a c be the Alvus of Urna, Frenum, Uncus, Spicula. Now, from a c d we have Urna, Frenum, Sector, Ostrum, Uncus, Ala, Bidens, Pallor, Cortis, Scena, Tergum, Aer, Vestis, Oliva, Tyro. From c d a we have Urna, Ostrum, Comes, Frenum, Uncus, Spicula, Plebs, Pallor, Mora, Sypho, Tergum, Oliva. In order to see how these will modify each other, let us consider the a c d solution as if it were a set of cubes in the c d a arrangement. Here, those that go in the Arctos direction, go away from the plane of projection, and must be represented by the Syce of the cube in contact with the plane. Looking at the a c d solution we write down (keeping those together which go away from the plane of projection): Urna and Ostrum, Frenum and Uncus, Sector and Ala, Bidens, Pallor, Cortis, Scena and Vestis, Tergum and Oliva, Aer and Tyro. Here we see that the whole c d a face is filled up in the projection, as far as this solution is concerned. But in the c d a solution we have only Syces of Urna, Frenum, Plebs, Sypho. These Syces only indicate the presence of a certain number of the cubes stated above as possible from the Moena projection, and those are Urna, Ostrum, Frenum, Uncus, Pallor, Tergum, Oliva. This is the result of a comparison of the Moena projection with the Syce projection. Now, writing these last named as they come in the d a c projection, we have Urna, Ostrum, Frenum, Uncus and Pallor and Tergum, Oliva. And of these Ostrum Alvus is wanting in the d a c projection as given above. Hence Ostrum will be wanting in the final shape, and we have as the final solution: Urna, Frenum, Uncus, Pallor, Tergum, Oliva.